How do you know why Rolle's Theorem does not apply to #f(x)= x^(2/3)# on the interval [-1,1]?
1 Answer
Apr 18, 2015
H1
Is the function continuous on the closed interval?
Yes, power functions are continuous on their domains.
H2
Is the function differentiable on the open interval?
No.
(By the way, H3
Also by the way: This function does not satisfy the conclusion of Rolle's Theorem on any interval, because there is no solution to: